Incongruity means out of place — something that doesn't fit in its location or situation. The art show patrons couldn't help but chuckle at the incongruity of a toilet sitting in the middle of an exhibition of Renaissance paintings.
An incongruity is very different from everything around it, to the point of being inappropriate to the situation. A cat at a dog's birthday party would be an incongruity, as would a pacifist at a meeting of the War Lovers' Society. Incongruity is the idea that something is incongruous, or inappropriate. A purple towel is an incongruity in an all black-and-white bathroom.